Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Polynomial time algorithms for network information flow
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
An algebraic approach to network coding
IEEE/ACM Transactions on Networking (TON)
Foundations and Trends® in Networking
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A Random Linear Network Coding Approach to Multicast
IEEE Transactions on Information Theory
On codes from norm-trace curves
Finite Fields and Their Applications
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Using tools from algebraic geometry and Gröbner basis theory we solve two problems in network coding. First we present a method to determine the smallest field size for which linear network coding is feasible. Second we derive improved estimates on the success probability of random linear network coding. These estimates take into account which monomials occur in the support of the determinant of the product of Edmonds matrices. Therefore we finally investigate which monomials can occur in the determinant of the Edmonds matrix.